Stability of \(L^\infty\) solutions for hyperbolic systems with coinciding shocks and rarefactions (Q2782964)

The author studied the hyperbolic system of conservation laws NEWLINE\[NEWLINEu_t+ f(u)_x= 0,\quad u(0,\cdot)= u_0,NEWLINE\]NEWLINE where each characteristic field is either genuine nonlinear or linearly degenerate. The main result is: under the assumption of coinciding shock and rarefaction curves and the existence of a set of Riemann coordinates, there exists a semigroup of solutions \(u(t)= S_t u_0\), defined on initial data \(u_0\in L^\infty\), the semigroup \(S\) is continuous w.r.t. time and the initial data in \(L^1_{\text{loc}}\) topology. Moreover, \(S\) is unique and its trajectories are obtained as limits of wave front tracking approximations.